Essential Spectral Properties of Third-Order Upper Triangular Relation Matrices

设 H 1 , H 2 , H 3 为无穷维复可分Hilbert空间，对给定关系 A∈ℬℛ( H 1 ),B∈ℬℛ( H 2 ),C∈ℬℛ( H 3 ) ，记 M D,E,F =( A D E 0 B F 0 0 C )∈ℬℛ( H 1 ⊕ H 2 ⊕ H 3 ) ，本文讨论了 D∈ℬℛ( H 2 , H 1 ) ， E∈ℬℛ( H 3 , H 1 ) ， F∈ℬℛ( H 3 , H 2 ) 时 M D,E,F 的本质谱、Weyl谱和本质近似点谱包含关系成立的条件。Let H 1 , H 2 , H 3 be infinite-dimensional complex separable Hilbert spaces, given the relation A∈ℬℛ( H 1 ),B∈ℬℛ( H 2 ),C∈ℬℛ( H 3 ) , and write M D,E,F =( A D E 0 B F 0 0 C )∈ℬℛ( H 1 ⊕ H 2 ⊕ H 3 ) . In this paper, a necessary and sufficient condition is given for the essential spectrum, Weyl spectrum, essential approximation point spectrum for M D,E,F with D∈ℬℛ( H 2 , H 1 ) , E∈ℬℛ( H 3 , H 1 ) , F∈ℬℛ( H 3 , H 2 ) .